Mathematical Cultures

The UK Arts and Humanities Research Council has agreed to fund a research network on mathematical cultures.  Here, I describe this project and what we hope to learn from it.

Why study mathematical cultures?  Why now?

Mathematics has universal standards of validity.  Nevertheless, there are local styles in mathematics.  These may be the legacy of a dominant individual (e.g. the Newtonianism of 18th century British mathematics).  Or, there may be social or economic reasons (such as the practical bent of early modern Dutch mathematics).

These local mathematical cultures are scientifically important because they can affect the direction of mathematical research.  They also matter because of the cultural importance of mathematics.  Mathematics enjoys enormous intellectual prestige, and has seen a growth of popular publishing, films about mathematicians, at least one novel and plays.  However, this same intellectual prestige encourages a disengagement from mathematics.  Ignorance of even rudimentary mathematics remains socially acceptable.  Policy initiatives to encourage the study of mathematics usually emphasise the economic utility of mathematics (for example the 2006 STEM Programme Report).  Appeals of this sort rarely succeed with students unless there is a specific promise of employment or higher remuneration.
What these political anxieties call for is a re-presentation of mathematics as a human activity, which means, among other things, that it is part of culture.  The tools and knowledge necessary for this have been developing in recent years.  Historians of mathematics have begun to consider mathematics in its social, political and cultural contexts.  There is now an established sociology of science and technology, published in journals such as Science as Culture and the Journal of Humanistic Mathematics.  Mathematics educationalists have begun to draw on some of these developments (particularly historical research).

In the philosophy of mathematics, there is now a sub-field devoted to the philosophy of mathematical practice.  So far, this has mostly emerged in continental Europe, and to a lesser extent in North America.  The Brussels-based Perspectives on Mathematical Practice initiative met in 2002 and 2007 and published proceedings.  The PhiMSAMP network (2005-2010) was a collaboration of researchers in several countries.  The annual Novembertagung on the history and philosophy of mathematics serves beginning researchers in philosophy and history of mathematics.  In France, there is a thriving Parisian history and philosophy of mathematics scene, and a mathematics thread in the studies of scientific practice at the Laboratoire d’Histoire des Sciences et de Philosophie (Nancy).  So far, philosophy of mathematical practice has not focussed on mathematics as culture.  This has prevented it from elaborating one possible answer to the student’s question, “why should I study mathematics?”, namely, “Because it is beautiful, glorious and deep”.  Grounding this answer requires an exploration of the value of mathematics and the values of mathematicians, and communicating this answer requires an understanding of mathematics as part of our larger contemporary culture.

What exactly will this project do?

This project will host three conferences.  The first (September 2012, at De Morgan House, London, UK) will explore and begin to map the variety of and connections among contemporary mathematical cultures.  These can be research cultures, but also include mathematical cultures among instructors and students.  The programme for the first conference is on the project website.

The second (September 2013) conference will articulate and classify mathematical values.  When mathematicians award or withhold prizes, scholarships, PhDs and grants, correctness is almost never the decisive criterion.  Rather, the question is whether the work is worthwhile, interesting, elegant, promising, insightful, etc..  If these judgments are not arbitrary, they should refer to some standards or values.  Are these standards or values common across all mathematical cultures?  How are they taught?  How do they evolve?  What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, ‘explanatory’, etc.?  What is the rational structure of the deliberations mathematicians use to reach value judgments (in PhD examinations, book reviews, journal referee reports, etc.)?  This conference will build on the first conference by referring these questions to the various mathematical cultures identified at that first event.

The third conference (Easter 2014) will discuss mathematics in public culture and mathematics as part of cultural wealth.  Amongst other topics, it will explore the question “why should I study mathematics?”  This third meeting will build on the first conference by identifying the contributions from and audiences in the various mathematical cultures.  It will build on the second conference by drawing on the articulations and explorations of mathematical values.

What will this achieve?

The main aim is to connect researchers on mathematical cultures who may not have encountered each other before.  The various disciplines (history, sociology, philosophy, cognitive science) have their distinct circuits and there are national and linguistic barriers too.

We also want to encourage some thinking about the methodological challenges facing the study of mathematics as culture.  Much of the philosophical interest in this area is in the question of how mathematics can be simultaneously culture and knowledge.

So far, we have established a programme for the first conference (September 2012).  Thanks to the AHRC, it will be very cheap to attend.  So if you are near London in September, do come along.

Brendan Larvor b.p.larvor >>at<< herts.ac.uk

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